Half of all Americans believe they are protected by guardian angels, one-fifth say they’ve heard God speak to them, one-quarter say they have witnessed miraculous healings, 16 percent say they’ve received one and 8 percent say they pray in tongues, according to a survey released Thursday by Baylor University.

The wide-ranging survey of 1,648 adults, who were asked 350 questions on their religious practices last fall, reveals a significant majority who are comfortable with the supernatural.

“Mystical experiences are widespread,” said Rodney Stark, co-director of Baylor University’s Institute for Studies of Religion.

“I’d have guessed 15 percent instead of 55,” he added, referring to the 55 percent who claimed angelic protection. “This is the taboo subject in American religion. No one studies it, but there is a lot of it out there.”

The survey, which has a margin of error of four percentage points, also revealed that theological liberals are more apt to believe in the paranormal and the occult - haunted houses, UFOs, communicating with the dead and astrology - than do conservatives. Women (35 percent), blacks (41 percent), those younger than 30 (40 percent), Democrats (40 percent) and singles who are cohabitating (49 percent) were more likely to believe, the survey said.

Baylor researchers also criticized a much-ballyhooed “new atheism” as a barely discernable trend, saying the number of Americans who are atheists has stayed at 4 percent since 1944.

Why? Atheism is a “godless revolution that never happened,” the survey said, adding that irreligion often is not effectively transmitted to children who, when they reach adulthood, often join conservative religious denominations.

Moreover, atheism is hardly taking over the world. Europe does have more atheists than the U.S., the survey said, but no country has more than 7 percent except France, which is at 14 percent of the populace. Farther to the east, Japan is at 12 percent and China is at 14 percent.

Mr. Stark dismissed the popularity of several recent books on atheism, saying they are mostly the products of “angry” people who are largely ignored by theists.

“The religious people don’t care about the irreligious people,” Mr. Stark said, “but the irreligious are prickly. I think they’re just angry.”

The survey also ranked church attendance at 36 percent of the populace, about eight percentage points lower than similar surveys by pollster George Gallup but more than the low 20th percentile suggested by other polls.

“There was only one decline in church attendance and that was in the late 1960s,” Mr. Stark said, “when the Vatican said it was not a sin to miss Mass. They said Catholics could act like Protestants, and so they did.”

When asked at a press conference whether he was certain that one-third of the American populace is in church every week, he allowed that some of the respondents in the poll might have exaggerated their attendance.

“I’d say 30 percent,” he said, “but it’s very high.”

The survey spoke highly of the American megachurch, congregations of more than 1,000 that are often criticized for their impersonal nature. People who attend megachurches are far more conservative in their theology than are attendees of smaller churches, it said.

Their members are also younger, they share their faith more with strangers, and they perform more volunteer work than do members of small churches.

“There are many critics who think the megachurches thrive on people who enjoy dramatic Sunday services with fine music but don’t wish to become very ‘religious’ on a day-to-day basis - that the megachurch appeal is a mile wide and an inch deep,” said “What Americans Really Believe,” a companion book to the survey.

“But it is not true. Those who belong to megachurches display as high a level of personal commitment as do those who attend small congregations.”

Mr. Stark added, “Apparently they are preaching Jesus and that’s why they get so big.”